1. Homework #3 Environment Lights
Digital Image Synthesis
Yu-Ting Wu

2. The brighter pixels (lights) have higher probability to be sampled
Project description
Pbrt uses run-time importance sampling to render scenes with environment lights
The details will be given when talking about Monte Carlo integration
In this homework, you are asked to provide an alternative approach
The brighter pixels (lights) have higher probability to be sampled

3. Project description
Represent the environment map with a set of point (directional) lights
A light probe image is subdivided into 64 equal-energy regions. A point light is created for each region at its centroid.

4. Project description Implement the “MedianCut” algorithm in pbrt
There are three functions you should modify:
Constructor
Do MedianCut algorithm to generate a set of lights with roughly equal energy
Sample_L
When pbrt asks a sample from environment light, uniformly select one from all lights and return its direction, intensity, and PDF
IsDeltaLight
Tell pbrt whether this light can be sampled or not?
For any other member functions, you can leave them alone at this time

5. Importance sampling
In rendering, one important question is how to determine the sample distributions
Importance sampling:
If the shape of sampling distribution is close to the shape of integrand, variance is reduced
In our case
Sample_L
Sample_f

6. Multiple importance sampling
Sample light or sample BRDF only cannot adapt to all configurations
Multiple importance sampling:
Generate one sample using Sample_L and another using Sample_f, then combine the sample results
Better than either of the two strategies alone
Sample Light
Sample BRDF
Multiple Importance Sampling

7. Multiple importance sampling
Codes for estimating direct lighting in pbrt:

8. Multiple importance sampling

9. Multiple importance sampling
IsDeltaLight
In homework #3, since we transform the environment to a set of directional lights which cannot be sampled, we should return true to avoid “BRDF importance sampling”
Sample_L
Pbrt only asks one sample at a time.
In homework #3, all lights have roughly equal energy.
We can simply random choose one from n lights and return PDF with 1/n

10. FAQ
The rendered images have different radiance scale to the reference ones
Each pixel in the environment map represents an area on unit sphere
Remember to scale the light intensity with the areas (solid angles)
width  2PI w
HeightPI h

11. Related papers Variance Minimization Light Probe Sampling
K. Viriyothai and P. Debevec
SIGGRAPH 2009 Poster
Structured Importance Sampling of Environment Maps
S. Agarwal, R. Ramamoorthi, S. Belongie, and H. W. Jensen
SIGGRAPH 2002
Efficient Illumination by High Dynamic Range Images
T. Kolling and A. Keller
EGSR 2003
Fast Hierarchical Importance Sampling with Blue Noise Properties
V. Ostromoukhov, C. Donohue, and P. –M. Hodoin
SIGGRAPH 2004